Hypothesis testing is an important step that researchers must test. Researchers will develop research hypotheses according to the points of research objectives. Furthermore, researchers will test the hypothesis using statistical methods so that the test results can be accounted for scientifically.
Before testing the hypothesis, researchers are expected to understand what a hypothesis is. The hypothesis is a brief statement from a study based on theory and empirical experience whose truth is still weak.
Research activities are needed to prove the hypothesis, starting from data collection, analysis, and statistical testing. Therefore, in statistical testing, it will be decided whether to accept the hypothesis or reject the hypothesis. To read other articles that discuss hypothesis testing, you can read my articles entitled: “How to write and test statistical hypotheses in simple linear regression” and “How does high variance affect hypothesis testing in linear regression?“
Stages of hypothesis testing
In Hypothesis Testing, researchers must carry out several stages, including establishing hypotheses, determining testing criteria, conducting statistical tests, establishing critical points, and determining conclusions. In creating the hypothesis, the researcher will divide the hypothesis into two, namely the null and alternative Hypotheses.
The null hypothesis is a statement tested for truth using statistical methods. The way of writing the null hypothesis will be different, for example, for regression analysis, correlation analysis, and different tests. Furthermore, the alternative hypothesis is a statement that is the opposite of the null hypothesis. When the null hypothesis is rejected in statistical testing, the alternative hypothesis will be accepted.
Generally, the hypothesis is divided into descriptive, comparative, and associative hypotheses. After the researcher creates the null and alternative hypotheses, the researcher needs to determine whether to use the one-tailed and two-tailed tests.
The two-tailed test is used when the researcher does not know the association sign of the analyzed variables. Conversely, if the researcher already knows the sign of the relationship, for example, positive or negative, then the researcher can use the one-tailed test.
In the next step, the researcher conducted statistical tests following the hypotheses that had been made. After statistical testing, for example, regression analysis, correlation analysis, and different tests, the next step is determining the critical point for hypothesis testing.
Alpha levels generally used in various fields of science are 1%, 5% and 10%. The determination of the alpha percentage is adjusted to the accuracy level in the study field. The final step is to conclude whether to accept or reject the null hypothesis. If the null hypothesis is rejected, then the alternative hypothesis is accepted.
Hypothesis test for regression analysis
I have prepared a Mini research example to make it easier to understand hypothesis testing for linear regression analysis. This study uses quarterly time series data from the 1st quarter of 2018 to the 3rd quarter of 2021.
Based on this research, the research objectives were formulated to determine the effect of advertising costs and marketing staff on product sales. In detail, the specification of the equation of the linear regression in this study can be seen as follows:
Y = b0 + b1X1 + b2X2 + e
Description,
Y = Product sales (dependent variable)
X1 = Advertising Cost (independent variable)
X2 = Marketing staff (independent variable)
b0 = Intercepts
b1, b2 = Regression estimation coefficients
e = Error terms
Based on these case examples, the researcher created null and alternative hypotheses. For example, I will prove the hypothesis that advertising costs affect product sales.
Therefore, I will create the following hypothesis:
Null Hypothesis (H0): β1 = 0, Advertising cost partially has no significant effect on product sales
Alternative hypothesis (H1/Ha): β1 ≠ 0, Advertising cost partially has a significant effect on product sales
In the same way, you can also create a hypothesis for the marketing staff variable partially on product sales. You can also make a hypothesis to prove that advertising costs and marketing staff simultaneously affect product sales.
On this occasion, I will give an example to test the hypothesis of the effect of advertising costs on product sales. Based on the results of multiple linear regression analysis, the output is as shown below:
Based on the image above, we focus on the part marked with an arrow. Following the hypothesis that has been created, the criteria for testing the hypothesis are as follows:
If the t-statistic <t critical, then the null hypothesis is accepted
If the t-statistic >= t critical, then the null hypothesis is rejected (accepts the alternative hypothesis)
In addition to comparing t-statistics with t critical, for testing the hypothesis, you can use the p-value. In the mini-research example using an alpha of 5%, the criteria for testing the hypothesis are:
If the p-value > 0.05, then the null hypothesis is accepted
If the p-value ≤ 0.05, then the null hypothesis is rejected (accept the alternative hypothesis)
Based on the analysis results, the advertising cost variable has an estimated coefficient value of 4.848 and a t-statistic of 4.2612. For hypothesis testing here, I will use the p-value.
The p-value of the advertising cost variable is 0.001105, indicating that the p-value is <0.05, so we reject the null hypothesis. Because we reject the null hypothesis, it means we accept the alternative hypothesis. Thus it can be concluded that advertising costs partially significantly affect product sales, furthermore, for testing other hypotheses in the regression analysis using the same method.
Hypothesis test for correlation analysis
In principle, hypothesis testing in correlation analysis is similar to hypothesis testing in linear regression analysis. Here I will give an example of a correlation test that uses variables measured on an ordinal scale.
Researchers collected cross-sectional data from 40 consumers. The purpose of this research is to find out the relationship between consumer behavior and purchase decisions. To test the hypothesis, researchers can make hypotheses as follows:
The null Hypothesis (H0): ρ = 0, Consumer behavior has no significant correlation with purchase decision
Alternative hypothesis (H1/Ha): ρ ≠ 0, Consumer behavior has a significant correlation with purchase decision
The criteria for testing the hypothesis in correlation analysis either use ρ value comparisons with the r table or by comparing the P-value with alpha in the same way as in the hypothesis testing sub-section for linear regression in the previous paragraph. The results of the correlation analysis of consumer behavior and purchase decisions using SPSS can be seen as follows:
Based on the picture above, it is known that the correlation coefficient of consumer behavior with purchase decisions is 0.741. Based on the p-value, which is less than 0.05, it can be concluded that the null hypothesis is rejected.
Because we reject the null hypothesis, we accept the alternative hypothesis. Therefore it can be concluded that consumer behavior significantly correlates with purchase decisions.
Hypothesis test for different tests
With the same principle, hypothesis testing on different tests can also be carried out based on comparing t-statistics with t-critical or the P-value with Alpha. For an example of a different test, I will compare the pre-test and post-test.
The researcher wants to know whether there is a difference between the mean pre-test and post-test. Researchers used a sample of 15 people. Before experimenting, the researcher conducted a pre-test on the 15 samples, then after conducting the experiment for three months, the researcher conducted a post-test on the same 15 samples.
To test the hypothesis, the researcher has created the following Hypothesis:
The null hypothesis (H0): µ1 = µ2, the mean pre-test and mean post-test are not significantly different
Alternative hypothesis (H1/Ha): µ1 ≠ µ2, the mean pre-test and mean post-test are significantly different
Next, the researcher conducted a different test using a paired sample t-test. The output of the paired sample t-test analysis using Excel can be seen in the image below:
Based on the picture above, the t-statistics value is 7.98226 > t critical is 2.145 or p-value < 0.05. Based on the same hypothesis testing criteria, the null hypothesis is rejected.
Because we reject the null hypothesis, we accept the alternative hypothesis. Therefore, it can be concluded that the mean pre-test and mean post-test are significantly different. The analysis showed that the mean post-test was higher than the mean pre-test.
Based on examples of hypothesis testing, both in regression analysis, correlation analysis, and different tests, we can learn that researchers should already understand how to test statistical hypotheses. It is an article that I can write on this occasion, and I hope it is helpful for all of you. Wait for the article update the following week. Thank you.
